We show the identification of the joint distribution of the potential outcomes under various parametric specifications. The key factor of the identification is the nonnormality of the distribution of the observed variables, with which we can obtain information of higher order moments that are not determined only by mean and variance. In particular, we show the identification of the joint distribution of the potential outcomes when it is specified by a normal mixture. Because any continuous distribution can be well approximated by a finite mixture distribution, our result may cover a wide class of distributions. The identification results derived are useful for estimating quantile treatment effects, causal mediation effects, and heterogeneous treatment effects, which cannot be estimated even if the unconfoundedness assumption is satisfied.

中文翻译：

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参数识别潜在结果的联合分布

我们展示了在各种参数规范下对潜在结果联合分布的识别。识别的关键因素是观测变量分布的非正态性，通过它我们可以获得不仅由均值和方差确定的高阶矩信息。特别是，当显示正常混合指定的结果时，我们显示了对潜在结果联合分布的识别。因为任何连续分布都可以通过有限的混合分布很好地近似，所以我们的结果可能涵盖了很宽的一类分布。得出的识别结果可用于估算分位数处理效果，因果中介效果和异构处理效果，即使满足无混淆性假设，也无法估计这些效果。